How do I graph #(x+2)^2/9+(y-3)^2/25=1# algebraically?

1 Answer
seph
Oct 8, 2014

You have an ellipse in the form

#(x - h)^2/b^2 + (y - k)^2/a^2 = 1#

where (h, k) is the ellipse's center.
You have #(-2, 3)# as your center.

#a# is under #y#. That means your major axis is vertical with length #2a = 10#.
The endpoints of your major axis are #(-2, -2)# and #(-2, 8)#

Meanwhile, the minor axis is horizontal with length #2b = 6#
The endpoints of your major axis are #(-5, 3)# and #(1, 3)#

Connect the endpoints of your major and minor axis and you have your ellipse

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